\(\blacksquare \)
Our analysis approaches the classification setting as a limit of the regression implicit bias. This argument gives stronger theoretical justification for utilizing the regularized direction (as employed by [1]}) and partially addresses the concern from [2]} that the implicit bias of regression and classification problems are “fundamentally different.”
\(\blacksquare \)
On a more technical note, analyzing the implicit bias requires handling the cross terms of the form \(\left\langle \nabla \psi (w),~ w^{\prime } \right\rangle \) , which lack direct geometric interpretations.
We demonstrate that for our potential functions of interest, these terms can be nicely written and can be handled in the analysis.

